Abstract
Using mathematical models to represent aspects of physical reality is an essential activity in science and science education. This contribution discusses four approaches of using computer programming and mathematical models in classroom activities:1) Mathematical models, found in the textbook, are used as a basis for computer programs. Students, when creating useful interactive python programs calculating concentrations or pH-values, experience similar intellectual challenges as in solving traditional text book problems.2) Scratch-animations simulating physical or chemical systems simulation can be specifically designed to check the validity of given mathematical models.3) A computer-related challenge is to design a simulation (like gas diffusion in a closed system with two phases) that might be a basis for discovering a mathematical model (like Henry's law) or just an element of a mathematical model.4) Using sensor technology and a Raspberry Pi, students create a computer program that automatically visualizes the observed system behaviour (like changes in gas concentrations) in order to find a mathematical model.
Highlights
Models of the physical reality that are taught in high school science lessons are represented by mathematical equations
2) Developing animations simulating physical or chemical systems in order to check the validity of given mathematical models
In the previous section we discussed the evaluation of computer simulations, which were based on simple assumptions like the the behaviour of gas molecules. mathematical models that are found by checking simulations are basically not more than logical deductions from the model the simulation is based upon
Summary
Models of the physical reality that are taught in high school science lessons are represented by mathematical equations. There exist special digital tools for performing simulations and discovering and exploring models. They can be grouped in two types:. Students use highly specialized software-tools only seldom Still they have to acquire technical knowledge to be able to handle the tool. The students need to develop general informatics competences before and during the project. This takes time and may require some “professional support” by a computer science teacher. Programming challenges can be designed in a way that mathematical modelling is involved. 2) Developing animations simulating physical or chemical systems in order to check the validity of given mathematical models. This contribution discusses four approaches of integrating computer programming and mathematical modeling in science education: 1) Using mathematical models as a basis for simple interactive Python programs. 2) Developing animations simulating physical or chemical systems in order to check the validity of given mathematical models. 3) Designing computer simulations in order to discover mathematical models. 4) Creating computer programs that automatically visualize sensor data and support checking mathematical models
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